You should notice that I use the word “trust”. I install stuff on my servers and PCs from people who I trust. Why should I trust someone who makes an anticheat engine. Why should I have a reason to do that?

You should also understand that a kernel-level piece of code that can be updated is a very good rootkit. It contains all essential tools to modify hardware, kernel, install drivers, keyloggers etc. It satisfies the definition of “rootkit” very well.

One single piece of code is enough to be a rootkit.

Also definition by antimalware vendors:
https://www.trendmicro.com/vinfo/us/security/definition/rootkit
https://www.kaspersky.com/resource-center/definitions/what-is-rootkit
https://learn.microsoft.com/en-us/sysinternals/downloads/rootkit-revealer#what-is-a-rootkit

Popular definition (e.g . Ionos):

Rootkits: The rootkit is considered to be a type of Trojan horse. Many Trojan horses exhibit the characteristics of a rootkit. The main difference is that rootkits actively conceal themselves in a system and also typically provide the hacker with administrator rights.